Understanding Residual Stress Evolution in Directed Energy Deposition With Interlayer Deformation

There is a great deal of interest in metal additive manufacturing (AM) from various industries including aerospace, marine, and automotive among others. This is due to several advantages that AM has over conventional manufacturing that have been extolled in the literature. One drawback of AM technologies is the development of significant residual stresses, which cause warpage during the build phase and reduce the fatigue life during service. In fusion-based AM technologies such as laser powder bed fusion (LPBF) and directed energy deposition (DED), the development of residual stresses is explained by two mechanisms—the temperature gradient model and the cool-down phase model [1–3].

Although detrimental residual stresses can be alleviated from a built component by employing a postprocess heat treatment cycle (generally termed stress relief), this is generally not desirable for materials that cannot be precipitation hardened. Heat treatment may lead to other undesirable effects on the microstructures such as grain growth, removal of strengthening cell walls, and removal of microstructural design elements. For example, the work of Aversa et al. [4] showed that for 316L fabricated by DED, most residual stresses could be relieved by applying a heat treatment of 800 °C; however, this came at the cost of reduced hardness and yield strength. Therefore, there is a significant interest in controlling the RS distribution in AM components without resorting to postprocessing stress relief.

One of the most common techniques to reduce RS is to reduce the thermal gradients in the AM process. Klingbeil et al. [5] showed that residual stress-induced warpage could be reduced by substrate preheating for a cladding process. Similar observations were made by Ali et al. [6] for an LPBF process with preheating. Corbin et al. [7], however, pointed out that the reduction of RS due to preheating was not always positive and depended on the substrate thickness. Besides simply preheating the substrate, dynamic methods of preheating have also been studied where secondary heating is performed on the fly. This typically has the advantage that it is not just limited to the substrate. This kind of process includes the use of a secondary laser [8–10] or induction heating [11–13] to reduce the thermal gradients present in the build. Such processes not only reduce thermal gradients but can also act as a partial in-situ stress relief to further reduce the RS.

More recently, researchers have also attempted to apply surface severe plastic deformation (SPD) technologies between built layers, including shot peening (SP), laser shock peening (LSP), and cold rolling. Such technologies are already industrially applied to the final surfaces of components, to induce near-surface compressive residual stresses and thereby improve fatigue life. By applying these processes between additively manufactured layers, the detrimental tensile RS inherent in the AM process could be compensated. In essence, these SPD processes were applied layer by layer to control bulk RS. Although some amount of success in controlling RS using secondary heating or appropriate scan strategy has been demonstrated, these methods can typically only reduce the magnitudes of tensile RS. They do not allow the tailoring of bulk RS profiles by inducing local compressive residual stresses (CRS). Interlayer SPD technologies thus represent an interesting alternative to achieve engineered residual stress profiles, as they can be used to introduce CRS near geometrical stress concentrations or other regions from where fatigue cracks are likely to originate. It should be highlighted that this approach is limited by the necessity of maintaining static equilibrium. CRS cannot be infinitely increased. Rather all CRS will be offset by balancing tensile residual stresses (TRS). The RS engineering approach is thus an attempt to allocate compressive and tensile residual stresses based on the geometrical and loading conditions, subject to static equilibrium.

Kalentics et al. [14–17] studied such a process on 316L steel and Ti6Al4V. They showed improved fatigue life and reduction in warpage. Their work found that by applying LSP “n” layers below the final built surface in LPBF, deeper CRS could be realized due to the accumulation of CRS from multiple LSPs. Their critical finding was that building subsequent layers on top of the LSPed surface did not introduce sufficient heat to relax the RS. The same conclusion was reached for AlSi10Mg fabricated via LPBF with interlayer LSP by a separate research group [18,19] which also found that the realization of a second “compressive hook” was possible [18]. These studies indicated the possibility of tailoring the RS profile over the entire spatial geometry of a part using LPBF with interlayer deformation.

Similar hybrid processes have been applied in DED processes as well [20–28], although these studies have largely focused on grain refinement, microstructure, and the reduction of defects. There has been limited investigation on the possibility of tailoring RS in DED with interlayer peening. The few studies that have investigated this have focused on near-surface RS [25,29,30]. Some work has also been done in DED with a small spot diameter [31–33]. This however may not be representative of the entire DED process window as DED processes often use larger laser spots and thicker layers to achieve high build rates.

Typical DED processes use higher laser power and slower scanning speeds than LPBF. This leads to more significant heating of the underlying substrate and previously deposited material. Additionally, there is no powder bed to conduct heat away in a DED process, which leads to greater heat retention. The overall result is that CRS introduced by interlayer deformation processes has to withstand a more severe heating cycle in DED than in LPBF. It is not trivial that the results will be identical between DED and LPBF.

In this work, we experimentally study the effect of interlayer deformation on the bulk residual stress in a laser-based DED process. We show that irrespective of residual stress magnitude and depth, residual stresses are relaxed by the deposition of subsequent layers, under the selected processing conditions, which is in stark contrast to the findings of existing literature on LPBF. We further discuss the mechanism of stress relief. Contrary to the generally accepted paradigm of RS being relaxed due to annealing affected by intrinsic heating during subsequent layer deposition, we find that annealing behavior alone is not sufficient to explain the stress relaxation.

Sample fabrication was done in four steps. In the first step, 10 layers of 316L stainless steel were built on cold rolled 316L steel substrates via laser-based directed energy deposition as detailed in Sec. 2.1.1. The samples were then allowed to cool to room temperature after which various surface deformation processes were applied to the top of the built tenth layer (see Sec. 2.1.2). The samples were then repositioned in the DED setup for the building of another 10 layers. The final built layer (twentieth) was then subjected to another deformation process which was the same as the process applied to the tenth layer. A total of four different types of interlayer process samples were realized. One further sample was built with 20 layers deposited continuously to represent a typical DED process. The final sample geometry produced was nominally a solid cuboid of the square cross section with a side length of 27 mm in the build plane and a height of 20 mm. The various sample types are summarized in Table 1.

Directed energy deposition (DED) was performed on the commercial platform Lasertec 65 3D (DMG Mori, Japan) with a 1064-nm wavelength Nd:YAG laser source. Laser power, scanning speed, and spot size used were 1200 W, 18.33 mm/s, and 3 mm, respectively. A bidirectional raster scanning strategy was used with a hatch spacing of 1.5 mm with successive layers rotated by 90 deg. The powder used was PowderRange 316L E [34] (Carpenter Additive, UK) and the powder flowrate was measured to be 15.6 g/min. Argon was used as both the shielding and the carrier gas. The nominal layer height was ∼1 mm.

The peening processes were all done in setups separate from the DED machine. The hybrid fabrication in this work is thus asynchronous as per the definition of Sealy et al. [35].

SP was done using cast steel shots (ASR 70) as the media at an Almen intensity of 0.19 mmA. LSP was performed in an I20-R200A LSP machine (Tyrida International, Singapore) using a nanosecond laser with a wavelength of 1064 nm and a pulse width of 18 ns. A pulse energy of 10 J and a spot size of 3 mm were used giving a peak power density of 7.86 GW/cm². Pulses were spaced 1.5 mm apart in both scanning and transverse directions. Water was used as a confining medium with no ablative coating, a process that is commonly referred to as laser shock peening without coating) [36]. Hammer peening (HP) was performed using the Ecopeen tool (Ecoroll, Germany), which was mounted onto a 5-axis robot (ABB, Switzerland). The tool insert had a radius of 3 mm. Impact energy, feed rate, and overlap distance used were 90 mJ, 61.97 mm/s, and 0.275 mm, respectively. The specific peening processes and process parameters were selected to achieve distinct residual stress profiles as confirmed in Sec. 3.1.

Two different techniques were used to characterize the residual stresses. Center hole drilling (CHD) was used to characterize the near-surface residual stresses imposed by the various peening processes, while the contour method (CM) was used to measure the bulk residual stresses over the entire part.

CHD is a semidestructive RS measurement technique where a hole is incrementally drilled into the part to be inspected. The presence of residual stresses in the part would lead to surface deformations, which if measured can be used to reconstruct the residual stress field at the drilled depth. This can be repeated over a range of depths to obtain a residual stress depth profile. In this work, CHD was performed using a Prism system (Stresstech, Finland), which utilizes electronic speckle pattern interferometry to measure surface movements. A drill of 2.4-mm diameter (Kennametal, USA) was used to drill the holes. The first six measurements were taken at intervals of 32 µm, the subsequent six at intervals of 64 µm, the subsequent four at intervals of 128 µm, and the final four at intervals of 256 µm. All CHD measurements were performed at the geometrical center of the samples' top surface.

The contour method is a destructive residual stress measurement technique that can reveal the residual stress state over a plane of interest. It relies on the measurement of elastic deformations which occur when a component with residual stresses is sectioned along a plane. The elastic deformations are then taken as boundary conditions to a finite element (FE) model, which can then be used to calculate the original residual stress state present in the part prior to sectioning [37,38]. Sectioning was done using a wire electrical discharge machine using “skim” cut settings so as to not introduce additional stresses. A point cloud of the cut surfaces was created using a confocal microscope (Keyence, Japan). The point cloud data were then input into pyCM [39], an open-source framework for the application of the contour method. Data processing including alignment, interpolation onto a common grid, meshing, and application of nodal boundary conditions was performed using the inbuilt functions in pyCM. The solution of the FE model was done using abaqus® software (Dassault Systemes, France).

The temperature history is critical to understanding the development of residual stresses in AM. An FE model was developed using the commercial package, abaqus^®, to predict the temperature-time history of various points under consideration and relate them to the residual stress observations made.

A schematic representation of the geometrical domain with a discretized mesh of the FE model is shown in Fig. 1. Only half the domain was considered by exploiting symmetry, to reduce computational time. A single track was modeled to understand the temperature-time history at various depths using the laser parameters in Sec. 2.1. It is implicitly assumed that most of the thermal-induced stress relaxation in a region occurs when the laser passes directly over it during the deposition of the immediately subsequent layer. This is because during this time the maximum thermal load will be imposed on the region. While laser scanning of adjacent regions or other layers may also cause some heating, the effects will be of much smaller magnitude.

Near the laser-irradiated area shown in Fig. 1(b), a refined mesh of 0.1 mm size was used. To improve the solution time, this refined mesh was only used around the laser-irradiated area and was allowed to get progressively coarser further away from the laser-irradiated area. Similarly, mesh refinement was also used in the z (depth direction) with the mesh being 0.1 mm near the top surface (irradiated area) and increasing with depth.

where T is the temperature in K. The melting point (liquidus), solidus, and latent heat of fusion are 1700 K, 1658 K, and 2.6 × 10⁵ J/kg, respectively [42,43]. To account for Marangoni flows without explicitly including them in the model, the enhanced conductivity approach [44–47] was used with an enhancement factor of 2.5. This means the thermal conductivity was raised by a factor of 2.5 times for all temperatures greater than the liquidus temperature to account for heat transfer from convective Marangoni flows. Temperature-time histories were extracted for nodes at various depths at the geometric center of the irradiated area.

The proceeding sections discuss various results from this work. Section 3.1 presents the residual stress depth profiles induced by the peening processes. These results present the preexisting residual stress state at the tenth layer prior to subsequent layers' deposition. Section 3.2 presents the bulk residual stress across the whole sample geometry as measured by CM. Section 3.3 presents the temperature-time histories imposed by subsequent layer deposition when the laser passes directly above the region of interest, as determined by the FE model. This prevents the thermal loads that the preexisting residual stresses from Sec. 3.1 need to withstand to enable residual stress engineering. Typical images of the fabricated samples are shown in Fig. 2.

Before understanding the effect of interlayer peening on the RS distribution, it is important to characterize the RS profiles induced by the various peening processes in the as-peened condition, i.e., without subsequent layer deposition. CHD was thus performed for each different type of surface (as built, SPed, HPed, and LSPed), and the results are presented in Fig. 3. CHD was not performed for the ILC sample as it is assumed that the as-deposited 20th layers for both would have a similar RS state. This, however, would not be the case for the bulk RS distribution. It should be noted that the results presented in Fig. 3 are in-plane measurements, i.e., normal to the build direction.

It was observed that the AB sample had no TRS present in the near-surface region, as measured by CHD. This could be due to heat accumulation and the relatively high laser power used, leading to smaller thermal gradients and slower cooling rates. A similar observation was made by Piscopo et al. [48], who observed that at higher laser powers, near-surface TRS measured by CHD reduced and became more compressive in nature.

Distinct RS profiles were achieved due to various peening processes. Two parameters are used here to describe the resulting RS profiles—the peak CRS and the depth of effect. Here, the depth of effect is defined as the depth up to which the RS in the peened sample remains more than 100 MPa in compression.

The SP induced a very high peak CRS (−1020 MPa), but the depth of effect was low (0.29 mm). LSP on the other hand induced a much lower peak CRS (−569 MPa), but the depth of effect was much greater (1.07 mm). HP induced the most significant residual stress effects with a peak CRS of −1401 MPa and a depth of effect 1.58 mm. The depths of effect reported here are calculated based on linear interpolation between the closest measured data points.

It is important to highlight the uncertainty associated with these RS measurements. The uncertainty in CHD is affected by a range of factors including instrumentation errors, operating procedure adopted, and operator expertise [49]. To ensure consistency, all CHD measurements were done using the same equipment and operator, following the same operating procedure. The uncertainty also varies with depth and was estimated by Ref. [50] to be ±96 MPa near the surface, reducing to ±25 MPa at a depth of greater than 1 mm. A similar degree of uncertainty can be assumed for the present results as well.

The contour method was used to establish the bulk residual stress state for all samples. Results were extracted from the complete FE model across the centerline (line with alternating dashes and dots) in Fig. 4(a)) and the results are shown in Fig. 4(b). These results are taken as representative of the bulk RS stress state and provide the variation of in-plane RS with z height. The sample was divided into five regions for ease of analysis and discussion as shown schematically by the dotted red boxes in Fig. 4(a).

The substrate regions of all five samples show virtually the same RS distribution. This is in line with expectations as all samples were built on nominally identical substrates. For the AB sample, the RS in the lower part of the build shows a tensile stress of less than 100 MPa. This reduces to marginally compressive toward the middle of the build and then back to tensile in the upper portion of the build. The RS for the AB sample is quite similar in distribution and magnitude to past work on DED of 316L by Guo et al. [51]. They are also of similar magnitude to the work by Aversa et al. [4]; however, their work only performed near-surface RS measurements so only limited comparison can be made.

For the other four samples (ILC, SPed, LSPed, and HPed), the macro trend for the RS distribution still follows a similar pattern; however, the magnitudes of both the CRS and TRS seem to be greater. There was no significant difference between the RS distributions of these four samples, except for the top-most region. We observe a slight compressive RS peak in the top-most region for the HPed and LSPed samples which is due to the peening process applied. There does seem to be a discrepancy compared to the CHD results presented in Fig. 3, with the magnitude of both being significantly lower. This, along with the fact that no CRS was seen for the SPed sample, is attributed to the limitation of the contour method in accurately reconstructing stress fields near the edges of samples. With the contour method, the region within 0.5 mm of the outer edge of a component is subject to increased uncertainty [37]. Since the peak CRS from the peening processes all lies within 0.5 mm of the peened surface, this could explain the discrepancies between CHD and CM.

Importantly, no CRS peak was observed in the interlayer processed regions of the SPed, LSPed, and HPed samples when compared to the ILC sample. Although it was predicted a priori that some part of the CRS induced by the peening processes would be relaxed by intrinsic heating during subsequent deposition, the results indicate all the CRS were nullified. This phenomenon was previously termed “thermal cancellation” in a numerical study performed by Madireddy et al. [52]. These results are in stark contrast to those of Kalentics et al. [15] who, for the same material, reported that not all peening-induced RS were relaxed by building subsequent layers in an LPBF process. The mechanisms of stress relaxation are further discussed in Sec. 4.

To relate the RS relaxation behavior to the temperature profile, FE modeling was carried out to predict the temperature-time history that the parts would have experienced under the present DED conditions. To reduce computational time only single-track simulation was done. All analysis was performed in the region just below this single track. As this is the region that experiences maximum thermal load during the laser scan, this would be the area of maximum stress relaxation. Snapshots of the temperature distribution at various times are presented in Fig. 5. In the top views (Figs. 5(a1)–5(c1)), a high-temperature molten pool can be clearly seen with an elongated tail behind. In the side views (Figs. 5(a2)–5(c2)), the same melt pool is visible with the temperature distribution as a function of depth also apparent.

From the finite element solution, temperature-time histories at selected nodes were extracted for further analysis. Specifically, the temperature-time histories at the mid-point of the scanning path (at model time t = 0.7366 s) were extracted from the surface node to a depth of 1.47 mm below the surface (total eight nodes). These results are presented in Fig. 6.

Figure 6(a) shows the maximum temperature achieved at various depths below the surface exposed to the DED laser source. This can be used to estimate the melt pool depth, as regions where the maximum temperature exceeds the liquidus temperature would make up the melt pool. The calculated melt pool depth based on this was 0.12 mm which agrees well with our past work using the same parameters where the melt pool was measured to be 132–142 µm [53]. Figure 6(b) shows the entire temperature-time history at various depths. As expected, the curve becomes flatter with increasing depth (lower peak temperature, slower cooling rate). The approximate time for exposure to elevated temperatures (here defined as temperature >500 K) was between 0.6 and 0.9 s. This indicates that any relaxation of peening-induced stresses that occurred because of thermal loads took place in less than 1 s.

According to past literature, the stress relaxation mechanism of the peening-induced stresses is the intrinsic heating affected by subsequent layer deposition [15,19,52]. When DED layers are deposited on peened layers, the peened areas are subjected to very high temperatures. This acts as an in-situ stress relief heat treatment and the peening-induced RS are removed.

Two pieces of information are required to analyze this—the temperature-dependent $σy$ and the temperature-dependent elastic modulus. Both $σy$ and elastic modulus decrease with an increase in temperature for metallic materials. If both decrease in the same ratio, then no RS relief will occur as no reduction in elastic strain limit will occur. Stress relief will occur only if the reduction in YS is proportionally greater than the reduction in modulus.

The prior RS induced by peening is known (by CHD) as a function of depth (Fig. 3). The maximum reduction in elastic strain limit is also known (Fig. 7). Thus, for each point along the depth profile, the RS relaxation due to reduction in yield strength can be estimated. The calculated data are presented in Fig. 8. The points lying within the remelted zone in the relaxed RS profiles were excluded as any peening-induced RS in these areas would have been completely removed during fusion. Discussion of “stress relaxation” is thus meaningless for these points. The presented results were divided into three zones for ease of discussion.

Zone 1 consists of the regions which underwent remelting. These were the areas that had the highest magnitudes of peening-induced CRS; however, since this zone would undergo melting during subsequent layer deposition, all peening-induced stresses would be lost. Peening-induced CRS were limited to zone 1 for the SPed sample, but not for the LSPed and HPed samples. Zone 3 was the zone of minimal stress relaxation due to the low starting magnitudes of RS and the lower witnessed temperatures in this zone.

Zone 2 consisted of moderate magnitude CRS for the HPed and LSPed samples. In this zone, the yield strength reduction mechanism predicts significant stress relief; however, crucially, the retained CRS are still higher than what was measured by the contour method (Fig. 4). As per the contour method, the maximum measured CRS for the interlayer peened samples was at most −100 MPa. On the other hand, the $σy$ reduction (annealing) mechanism predicts that there still exist CRS of ∼200 MPa and ∼400 MPa for the LSPed and HPed samples respectively, over a depth of ∼0.7 mm. This is within the resolution of the contour method and would have been picked up if the RS predictions were correct. From this observation, it can be concluded that thermal annealing and the associated yield strength reduction cannot fully explain the relaxation of peening-induced residual stresses during subsequent layer deposition. There should be some additional mechanism involved.

It should be noted that the above discussion relies on a “point-by-point” method of calculating RS relaxation. Although such a method is computationally simple, it does not account for equilibrium considerations and so will not yield an exact result. To evaluate the magnitude of error associated with this simplification, a comparison was done between stress relaxation predicted by the above-described “point by point” method and commercial software (abaqus®)-based FEM. For the FEM, the initial RS distribution was prescribed and then subjected to the same thermal loads described in Sec. 2.3. The results depicted in Fig. 8(b) show minor differences between the “point-by-point” method and FEM with a maximum difference of 20% and a similar trendline.

The above discussion on RS relief ignores a critical aspect of the DED process—the highly localized nature of the temperature fields. The yield strength reduction model assumed that the entire part was heated uniformly. In such a case, the total strain increment would exactly equal the increment in thermal strain and stress relaxation would occur only due to yielding at a reduced elastic strain limit. It may be more appropriate to instead adopt the bar-frame framework [41], which mirrors the localized temperature loads, constrained by the surrounding, cold, bulk material. Figure 9 demonstrates the development of RS during one heating and cooling cycle in AM, according to the bar-frame model. The red central bar is the region that is subjected to thermal loads (and will undergo thermal straining) while the blue portion is assumed to be a cold, rigid frame that will constrain the red bar such that its total strain is constant. The dashed rectangular regions shown in Fig. 9 indicates the geometry the central bar would have assumed had it been able to expand and contract freely.

To demonstrate the various strains being developed over the thermal cycle, one cycle of heating and cooling is described using representative property values for 316L steel (σ_y = 500 MPa, elastic modulus = 193 GPa, coefficient of thermal expansion = 1.98 × 10⁻⁵ K⁻¹). The maximum temperature attained during the thermal cycle was taken to be 1623 K, which is the peak temperature achieved 0.192 mm below the top surface (Fig. 6). Strain-hardening and microstructural effects were excluded for simplicity.

Stage 0 is the starting stage where it is assumed that no strains exist in the material. As the central bar starts to heat up, it expands due to thermal expansion. The frame provides restraint, and the bar is loaded elastically in compression until its elastic strain limit. This occurs at 424 K (stage 1). After the elastic strain limit has been achieved, the bar continues to expand due to further heating. To accommodate the thermal strains being developed, the bar now yields in compression and plastic compression strains are developed. This occurs until the maximum thermal expansion occurs at 1623 K (stage 2). Subsequently, the material starts to contract due to cooling and first unloads elastically reducing the compressive elastic strain. The elastic unloading continues until the elastic strain is 0 (at 1361 K). Beyond this, further contraction of the central bar will start to load the bar elastically in tension, until the elastic strain limit (stage 3). The bar will continue to contract due to cooling; however, since the elastic tensile limit has been reached, further reduction in thermal strain will be offset by a reduction in the compressive plastic strain. This will continue until the thermal cycle is complete and the thermal strain has returned to 0. At this point, the bar has been plastically shortened and is under tensile elastic residual stress (stage 4).

The situation is slightly different where peening has been performed prior to the thermal cycle. Peening induces CRS by plastically stretching the near-surface region of the peened surface. The surrounding bulk restrains the expansion and leads to CRS being developed in the peened areas [66–68]. Figure 10 shows the development of RS in one heating cycle with preexisting CRS. For simplicity, it is assumed here that the preexisting RS is at the yield point and the material is elastic-perfectly plastic, i.e., no strain hardening.

In stage 0, unlike the AM-only case, the central bar is plastically stretched. This causes the surrounding rigid frame to induce a compressive elastic strain in the bar. When the bar starts to expand due to heating, none of the thermal strain that is developed can be accommodated by elastic compression. Instead, as soon as the temperature starts to increase (along with thermal strain), the bar starts to be plastically compressed, i.e., a reduction in the preexisting tensile plastic strain. This goes on until the plastic strain has reached 0 (stage 1) and then continues until the thermal tensile strain reaches its peak value at the maximum temperature of 1623 K (stage 2). It can be easily seen that despite the preexisting strains in the central bar, the bar in stage 1 and stage 2 is in identical stress condition to that in Fig. 9. Following the same thermal cycle in stages 3 and 4 will result in the same outcome and hence the same final RS condition. In effect, the plastic tensile strain induced by peening is consumed by the plastic compression induced by the thermal expansion. and there is no net change. The only way to avoid this and achieve “RS preservation” is to use a process window such that the thermal strain induced during stage 1 and 2 expansion is less than the plastic tensile strain induced by the peening process. For the situation shown in Fig. 10, this means that the maximum temperature experienced should be 424 K or less, as at this temperature, all plastic tensile strain is consumed by the thermal expansion.

The above discussion does not include the effect of strain hardening. Strain hardening induced by peening would lead to a larger elastic strain limit in going from stage 0 to stage 1 (Fig. 10). This means the central bar would be able to stay in the elastic zone up to a relatively higher temperature. However, unless the temperature witnessed was low enough that preexisting plastic tensile strain was not completely removed, the peening-induced CRS would not be maintained.

While the above discussion provides a phenomenological explanation of the stress relaxation mechanism, the situation is more complicated due to the presence of temperature dependence on the coefficient of thermal expansion (CTE) and the triaxial state of stress (the above discussion considers only the uniaxial case). To demonstrate the same principle considering the complete stress field, a coupled temperature-displacement FE simulation was performed. The same thermal loads from Sec. 3.3 were imposed on a substrate containing peening-induced RS. The peening RS were applied in the central portion as shown in Fig. 11(a). Two simulations were performed—one with temperature-dependent CTE from Ref. [69] and the second with the CTE set to zero. The results are presented in Fig. 11.

The von Mises effective stress distributions in Figs. 11(a)–11(c) indicate that the thermal strain is a critical factor affecting the development of residual stress relaxation. There is only a marginal difference in the von Mises RS distribution between initial peening RS and after laser pass with CTE = 0. On the other hand, the RS distribution after laser pass with temperature-dependent CTE shows a clear difference. Figure 11(d) shows the variation of in-plane RS along the depth for a typical section. Initially, the RS is compressive due to peening. The simulation where CTE was set to 0 shows only a marginal reduction in peening-induced CRS while the simulation with the temperature-dependent CTE shows a complete elimination of peening-induced CRS and conversion into TRS. This indicates that the phenomenological explanation depicted in Figs. 9 and 10 is valid even when extended to a three-dimensional stress state.

The results here indicate that RS preservation in DED is a challenge while previous work in LPBF has shown the possibility of modifying RS profiles by interlayer peening [15–18]. The reason why RS preservation is easier in LPBF is due to the difference in scale of the induced thermal field. A similar FE temperature model was developed using the laser parameters in the study by Kalentics et al. [15] to compare the temperature profile in their work to the present work. For this model, due to the much smaller spot size in LPBF, the mesh size had to be further reduced. A comparison of the FE temperature profiles is presented in Fig. 12. The results indicate clearly the significantly larger temperature affected zone in the DED process of the current work (Fig. 12(b)) as compared to the LPBF process of the past work [15] (Fig. 12(a)).

Although the peak temperature is higher, the distribution of thermal energy is highly localized. When viewed on the same spatial scale as DED, it is almost not visible. This is due to the fact that the heat flux is focused into a very small spot of 0.09 mm. This difference in thermal penetration is the primary reason for the difference in RS behavior between LPBF and DED with interlayer peening. It should be highlighted that these specific results are based on the individual process parameters used. However, they can be extrapolated to other parameter sets given the differences between LPBF and DED. In general, LPBF uses a lower laser power, smaller spot size, and higher scanning speed than DED [70] resulting in cooling rates much higher than in DED [71]. The meltpool in LPBF is also shallower and longer leading to greater amount of heat loss by convection rather than being conducted into the part [41]. The conditions in DED thus involve greater amount of thermal energy penetrating into the part leading to a greater propensity for stress relaxation. Future work will attempt to generalize this across material systems and derive relationships between the relaxation of peening-induced RS and combined process signatures such as volumetric energy density, normalized energy density, or normalized enthalpy.

In this work, the RS relaxation in a DED process with interlayer peening was investigated. Contrary to the literature on LPBF, complete relaxation of RS occurred after the deposition of subsequent layers. This was attributed to the significantly different thermal penetration in DED as compared to LPBF. Although peak temperatures were higher in LPBF, the thermal loads imposed are highly localized. This allows CRS, which are induced deeper in the material, to be insulated from the layers deposited subsequently. On the other hand, in DED, high thermal loads were present at all points within the CRS-affected depth, to the extent that all CRS was relaxed.

The mechanism of RS relaxation in such a hybrid process was clarified via thermal modeling. It was found that a simple stress relief or heat treatment mechanism (due to yield strength reduction) was insufficient to explain the RS relaxation. Rather, the localized temperature field causes localized thermal expansion, which is restricted by the surrounding cold bulk leading to redistribution of strains and thus stress relief. The preexisting tensile plastic strain induced by peening (which is responsible for CRS) is consumed by thermal strain during subsequent layer deposition leading to no CRS being preserved in the final build.

The findings in this work highlight the challenges with RS preservation in DED and provide some insight into how this can be achieved. The most obvious way would be to reduce the thermal penetration depth; however, this may not be possible for DED processes. Other ways could be to reduce the thermal gradient as the major stress relaxation mechanism is not peak temperature but thermal strain, which is affected by the thermal gradient. Materials with lower CTEs may also be a better option as thermal strain magnitudes would be lower. Future work will explore some of these possibilities with the objective of preserving peening-induced CRS during subsequent layer deposition. This could pave the way for residual stress engineering over bulk components by imposing RS fields to counter the effects of geometric stress concentrators.

The funding support from the Advanced Remanufacturing Technology Centre (ARTC), Singapore, via project agreement with Nanyang Technological University, Singapore, is gratefully acknowledged. AM thanks A*Star Graduate Academy (AGA) for financial support in the form of a PhD scholarship. The authors thank Mr. Guo Yong Chia and Mr. Aldrich Chua for assistance with the DED and shot peening processes respectively. The authors thank Professor Michael Fitzpatrick for discussions regarding the contour method. The authors also thank Ms. Thivyaa Ramesh and Mr. Vijay Shankar Sridharan for helpful comments.

AM: conceptualization, formal analysis, investigation, methodology, writing—original draft; NM: conceptualization, supervision, resources, writing—review and editing; NYJT: resources, writing—review and editing; YC: resources, writing—review and editing, supervision; SI: resources, writing—review and editing, supervision, project administration.

There are no conflicts of interest.

The datasets generated and supporting the findings of this article are obtainable from the corresponding author upon reasonable request.

c =

specific heat capacity

k =

thermal conductivity

r =

laser beam radius

E =

Young's modulus

P =

laser power

T =

temperature

T_m =

melting temperature

T_r =

reference temperature for Johnson-Cook yield criterion

A, B, C, n, m =

Johnson-Cook yield criterion parameters

Ab =

absorptivity

AM =

additive manufacturing

CHD =

central hole drilling

CM =

contour method

CRS =

compressive residual stresses

CTE =

coefficient of thermal expansion

DED =

directed energy deposition

FE =

finite element

HP =

hammer peening

ILC =

interlayer cooled

LPBF =

laser powder bed fusion

LSP =

laser shock peening

RS =

residual stress

SP =

shot peening

SPD =

severe plastic deformation

TRS =

tensile residual stress

(x,y) =

geometrical coordinates

$ε˙0$ =

reference strain rate for Johnson-Cook

ɛ_e =

elastic strain

ɛ_p =

plastic strain

ɛ_h =

thermal strain

ɛ_tot =

total strain

ɛ_v =

transformation strain

σ_y =

yield strength

φ =

heat flux